Correction: Evaporation-driven liquid flow in sessile droplets.

Correction for 'Evaporation-driven liquid flow in sessile droplets' by Hanneke Gelderblom et al., Soft Matter, 2022, 18, 8535-8553, https://doi.org/10.1039/D2SM00931E.

Evaporation-driven liquid flow in sessile droplets.

The evaporation of a sessile droplet spontaneously induces an internal capillary liquid flow. The surface-tension driven minimisation of surface area and/or surface-tension differences at the liquid-gas interface caused by evaporation-induced temperature or chemical gradients set the liquid into motion. This flow drags along suspended material and is one of the keys to control the material deposition in the stain that is left behind by a drying droplet. Applications of this principle range from the control of stain formation in the printing and coating industry, to the analysis of DNA, to forensic and medical research on blood stains, and to the use of evaporation-driven self-assembly for nanotechnology. Therefore, the evaporation of sessile droplets attracts an enormous interest from not only the fluid dynamics, but also the soft matter, chemistry, biology, engineering, nanotechnology and mathematics communities. As a consequence of this broad interest, knowledge on evaporation-driven flows in drying droplets has remained scattered among the different fields, leading to various misconceptions and misinterpretations. In this review we aim to unify these views, and reflect on the current understanding of evaporation-driven liquid flows in sessile droplets in the light of the most recent experimental and theoretical advances. In addition, we outline open questions and indicate promising directions for future research.

Evaporation of a Sessile Colloidal Water-Glycerol Droplet: Marangoni Ring Formation.

The transport and aggregation of particles in suspensions is an important process in many physicochemical and industrial processes. In this work, we study the transport of particles in an evaporating binary droplet. Surprisingly, the accumulation of particles occurs not only at the contact line (due to the coffee-stain effect) or at the solid substrate (due to sedimentation) but also at a particular radial position near the liquid-air interface, forming a "ring", which we term as the Marangoni ring. The formation of this ring is primarily attributed to the solutal Marangoni flow triggered by the evaporation dynamics of the water-glycerol droplet. Experiments and simulations show fair agreement in the volume evolution and the general structure of the solutal Marangoni flow, that is, the Marangoni vortex. Experiments show that the location of the Marangoni ring is strongly correlated with the Marangoni vortex. However, finite element numerical simulations fail to describe the particle distribution seen in the experiments. Interestingly, the particles not only accumulate to form the Marangoni ring but also assemble as colloidal crystals close to the liquid-air interface, yielding iridescence. The formation of the colloidal crystals in the experiments is strong evidence that non-hydrodynamic interactions, which are not represented in the simulations, also play a significant role in our system.

Periodic bouncing of a plasmonic bubble in a binary liquid by competing solutal and thermal Marangoni forces.

The physicochemical hydrodynamics of bubbles and droplets out of equilibrium, in particular with phase transitions, display surprisingly rich and often counterintuitive phenomena. Here we experimentally and theoretically study the nucleation and early evolution of plasmonic bubbles in a binary liquid consisting of water and ethanol. Remarkably, the submillimeter plasmonic bubble is found to be periodically attracted to and repelled from the nanoparticle-decorated substrate, with frequencies of around a few kilohertz. We identify the competition between solutal and thermal Marangoni forces as the origin of the periodic bouncing. The former arises due to the selective vaporization of ethanol at the substrate's side of the bubble, leading to a solutal Marangoni flow toward the hot substrate, which pushes the bubble away. The latter arises due to the temperature gradient across the bubble, leading to a thermal Marangoni flow away from the substrate, which sucks the bubble toward it. We study the dependence of the frequency of the bouncing phenomenon from the control parameters of the system, namely the ethanol fraction and the laser power for the plasmonic heating. Our findings can be generalized to boiling and electrolytically or catalytically generated bubbles in multicomponent liquids.

Marangoni Instability of a Drop in a Stably Stratified Liquid.

Marangoni instabilities can emerge when a liquid interface is subjected to a concentration or temperature gradient. It is generally believed that for these instabilities bulk effects like buoyancy are negligible compared to interfacial forces, especially on small scales. Consequently, the effect of a stable stratification on the Marangoni instability has hitherto been ignored. Here, however, we show that they can matter. We report, for an immiscible drop immersed in a stably stratified ethanol-water mixture, a new type of oscillatory solutal Marangoni instability that is triggered once the stratification has reached a critical value. We experimentally explore the parameter space spanned by the stratification strength and the drop size and theoretically explain the observed crossover from levitating to bouncing by balancing the advection and diffusion around the drop. Finally, the effect of the stable stratification on the Marangoni instability is surprisingly strongly amplified in confined geometries, leading to an earlier onset.

Evaporating droplets on oil-wetted surfaces: Suppression of the coffee-stain effect.

The evaporation of suspension droplets is the underlying mechanism in many surface-coating and surface-patterning applications. However, the uniformity of the final deposit suffers from the coffee-stain effect caused by contact line pinning. Here, we show that control over particle deposition can be achieved through droplet evaporation on oil-wetted hydrophilic surfaces. We demonstrate by flow visualization, theory, and numerics that the final deposit of the particles is governed by the coupling of the flow field in the evaporating droplet, the movement of its contact line, and the wetting state of the thin film surrounding the droplet. We show that the dynamics of the contact line can be tuned through the addition of a surfactant, thereby controlling the surface energies, which then leads to control over the final particle deposit. We also obtain an analytical expression for the radial velocity profile which reflects the hindering of the evaporation at the rim of the droplet by the nonvolatile oil meniscus, preventing flow toward the contact line, thus suppressing the coffee-stain effect. Finally, we confirm our physical interpretation by numerical simulations that are in qualitative agreement with the experiment.

Bouncing Oil Droplet in a Stratified Liquid and its Sudden Death.

Droplets can self-propel when immersed in another liquid in which a concentration gradient is present. Here we report the experimental and numerical study of a self-propelling oil droplet in a vertically stratified ethanol-water mixture: At first, the droplet sinks slowly due to gravity, but then, before having reached its density matched position, jumps up suddenly. More remarkably, the droplet bounces repeatedly with an ever increasing jumping distance, until all of a sudden it stops after about 30 min. We identify the Marangoni stress at the droplet-liquid interface as responsible for the jumping: its strength grows exponentially because it pulls down ethanol-rich liquid, which in turn increases its strength even more. The jumping process can repeat because gravity restores the system. Finally, the sudden death of the jumping droplet is also explained. Our findings have demonstrated a type of prominent droplet bouncing inside a continuous medium with no wall or sharp interface.

Gravitational Effect in Evaporating Binary Microdroplets.

The flow in an evaporating glycerol-water binary submillimeter droplet with a Bond number Bo≪1 is studied both experimentally and numerically. First, we measure the flow fields near the substrate by microparticle image velocimetry for both sessile and pendant droplets during the evaporation process, which surprisingly show opposite radial flow directions-inward and outward, respectively. This observation clearly reveals that in spite of the small droplet size, gravitational effects play a crucial role in controlling the flow fields in the evaporating droplets. We theoretically analyze that this gravity-driven effect is triggered by the lower volatility of glycerol which leads to a preferential evaporation of water then the local concentration difference of the two components leads to a density gradient that drives the convective flow. We show that the Archimedes number Ar is the nondimensional control parameter for the occurrence of the gravitational effects. We confirm our hypothesis by experimentally comparing two evaporating microdroplet systems, namely, a glycerol-water droplet and a 1,2-propanediol-water droplet. We obtain different Ar, larger or smaller than a unit by varying a series of droplet heights, which corresponds to cases with or without gravitational effects, respectively. Finally, we simulate the process numerically, finding good agreement with the experimental results and again confirming our interpretation.

Self-propulsion of inverse Leidenfrost drops on a cryogenic bath.

When deposited on a hot bath, volatile drops are observed to stay in levitation: the so-called Leidenfrost effect. Here, we discuss drop dynamics in an inverse Leidenfrost situation where room-temperature drops are deposited on a liquid-nitrogen pool and levitate on a vapor film generated by evaporation of the bath. In the seconds following deposition, we observe that the droplets start to glide on the bath along a straight path, only disrupted by elastic bouncing close to the edges of the container. Initially at rest, these self-propelled drops accelerate within a few seconds and reach velocities on the order of a few centimeters per second before slowing down on a longer time scale. They remain self-propelled as long as they are sitting on the bath, even after freezing and cooling down to liquid-nitrogen temperature. We experimentally investigate the parameters that affect liquid motion and propose a model, based on the experimentally and numerically observed (stable) symmetry breaking within the vapor film that supports the drop. When the film thickness and the cooling dynamics of the drops are also modeled, the variations of the drop velocities can be accurately reproduced.

Evaporation-Triggered Segregation of Sessile Binary Droplets.

Droplet evaporation of multicomponent droplets is essential for various physiochemical applications, e.g., in inkjet printing, spray cooling, and microfabrication. In this work, we observe and study the phase segregation of an evaporating sessile binary droplet, consisting of a miscible mixture of water and a surfactantlike liquid (1,2-hexanediol). The phase segregation (i.e., demixing) leads to a reduced water evaporation rate of the droplet, and eventually the evaporation process ceases due to shielding of the water by the nonvolatile 1,2-hexanediol. Visualizations of the flow field by particle image velocimetry and numerical simulations reveal that the timescale of water evaporation at the droplet rim is faster than that of the Marangoni flow, which originates from the surface tension difference between water and 1,2-hexanediol, eventually leading to segregation.

Self-wrapping of an ouzo drop induced by evaporation on a superamphiphobic surface.

Evaporation of multi-component drops is crucial to various technologies and has numerous potential applications because of its ubiquity in nature. Superamphiphobic surfaces, which are both superhydrophobic and superoleophobic, can give a low wettability not only for water drops but also for oil drops. In this paper, we experimentally, numerically and theoretically investigate the evaporation process of millimetric sessile ouzo drops (a transparent mixture of water, ethanol, and trans-anethole) with low wettability on a superamphiphobic surface. The evaporation-triggered ouzo effect, i.e. the spontaneous emulsification of oil microdroplets below a specific ethanol concentration, preferentially occurs at the apex of the drop due to the evaporation flux distribution and volatility difference between water and ethanol. This observation is also reproduced by numerical simulations. The volume decrease of the ouzo drop is characterized by two distinct slopes. The initial steep slope is dominantly caused by the evaporation of ethanol, followed by the slower evaporation of water. At later stages, thanks to Marangoni forces the oil wraps around the drop and an oil shell forms. We propose an approximate diffusion model for the drying characteristics, which predicts the evaporation of the drops in agreement with experiment and numerical simulation results. This work provides an advanced understanding of the evaporation process of ouzo (multi-component) drops.

Evaporation-triggered microdroplet nucleation and the four life phases of an evaporating Ouzo drop.

Evaporating liquid droplets are omnipresent in nature and technology, such as in inkjet printing, coating, deposition of materials, medical diagnostics, agriculture, the food industry, cosmetics, or spills of liquids. Whereas the evaporation of pure liquids, liquids with dispersed particles, or even liquid mixtures has intensively been studied over the past two decades, the evaporation of ternary mixtures of liquids with different volatilities and mutual solubilities has not yet been explored. Here we show that the evaporation of such ternary mixtures can trigger a phase transition and the nucleation of microdroplets of one of the components of the mixture. As a model system, we pick a sessile Ouzo droplet (as known from daily life-a transparent mixture of water, ethanol, and anise oil) and reveal and theoretically explain its four life phases: In phase I, the spherical cap-shaped droplet remains transparent while the more volatile ethanol is evaporating, preferentially at the rim of the drop because of the singularity there. This leads to a local ethanol concentration reduction and correspondingly to oil droplet nucleation there. This is the beginning of phase II, in which oil microdroplets quickly nucleate in the whole drop, leading to its milky color that typifies the so-called "Ouzo effect." Once all ethanol has evaporated, the drop, which now has a characteristic nonspherical cap shape, has become clear again, with a water drop sitting on an oil ring (phase III), finalizing the phase inversion. Finally, in phase IV, all water has evaporated, leaving behind a tiny spherical cap-shaped oil drop.